Simplify. Rewrite the expression in the form $x^n$. $x^3\cdot x^4=$
$\begin{aligned} x^3\cdot x^4&=x^{3+4} \\\\ &=x ^7 \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} x^3\cdot x^4&=\underbrace{x\cdot x\cdot x}_\text{3 times}\cdot\underbrace{x\cdot x\cdot x\cdot x}_\text{4 times} \\\\\\ &=\underbrace{x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}_\text{7 times} \\\\ &=x^7 \end{aligned}$ In conclusion, $x^3\cdot x^4=x^7$.